This book introduces the general theory of relativity and develops some elementary physical applications. The treatment is more sophisticated than most textbooks, particularly in the chapters that introduce the mathematical concepts needed to discuss the theory. Chapter 1 introduces special relativity, the Lorentz group, and contains some historical discussion of the origins of the theory. Chapter 2 introduces manifolds and fiber bundles, including homotopy and homology. Chapter 3 discusses connections and metrics, including connections on fiber bundles, Ehresmann connections, magnetic monopoles, affine connections and geodesics in Lorentzian and Riemannian manifolds. Chapter 4 covers the motion of a test particle in the Schwarzschild metric, periastron advance and the deflection of light rays. Chapter 5 talks about the Einstein equations and compares them and relates them to the Yang-Mills field equations, discussing the weak field limit, the graviton and the bottom up approach to the equations of Feynman and derives the Schwarzschild solution to the equations. Chapter 6 is about stellar equilibrium, talking about the interior solution and stellar stability, the Chandrasekhar mass limit and polytropes. Chapter 7 covers gravitational waves, including gravitational wave detectors, the emission of waves, the quadrupole formula and the binary pulsar. There are two appendices, the first one about spinors and the Clifford algebra, Majorana, Weyl spinors and the Dirac matrices. The second appendix covers Mathematica packages that are provided as supplementary materials in the publisher’s website.